A258842 Quasi-Carmichael numbers to exactly eight bases.

182293, 6536953, 13116283, 23337661, 55898473, 56624329, 66112261, 66355291, 66846751, 67239919, 75289033, 76222261, 93331321, 97594157, 110397013, 115175383, 146385797, 147111617, 157333573, 158029141, 159289241, 163825601, 181950817, 187826449, 207820831

Offset: 1

Author

Tim Johannes Ohrtmann, Jun 12 2015

Keywords

• nonn

Comments

All known terms have only two prime factors whereby the second prime factor is only slightly larger than the first.

a(3384) > 10^12. - Hiroaki Yamanouchi, Sep 26 2015

Examples

			a(1) = 182293 because this is the first squarefree composite number n such that exactly eight integers except 0 exist such that for every prime factor p of n applies that p+b divides n+b (-419, -418, -413, -412, -405, -403, -373, -349): 182293=421*433 and 2, 14 both divide 181874 and 3, 15 both divide 181875 and 8, 20 both divide 181880 and 9, 21 both divide 181881 and 16, 28 both divide 181888 and 18, 30 both divide 181890 and 48, 60 both divide 181920 and 72, 84 both divide 181944.
		

Links

• Hiroaki Yamanouchi, Table of n, a(n) for n = 1..3383

Crossrefs

Cf. A257750 (every number of bases).

Cf. A257751, A257752, A257753, A257754, A257755, A257756, A257757 (1 to 7 bases).

Cf. A257758 (first occurrences).

Programs

PARI

for(n=2, 1000000, if(!isprime(n), if(issquarefree(n), f=factor(n); k=0; for(b=-(f[1, 1]-1), n, c=0; for(i=1, #f[, 1], if((n+b)%(f[i, 1]+b)>0, c++)); if(c==0, if(!b==0, k++))); if(k==8, print1(n, ", ")))))

Extensions

a(4)-a(25) from Hiroaki Yamanouchi, Sep 26 2015